Not only is Carmelo Anthony torn up over missing the playoffs for the first time in his career, but for the second straight season, he finished the season playing with a torn shoulder. Whether he’s finished with the Knicks is another matter.

Although not as severe as last season’s injury, Tuesday’s MRI exam revealed Anthony has a small tear in the labrum of his right shoulder but it won’t need surgery at this point, the Knicks announced. Anthony, who sat out last night’s 109-98 win over the Nets, also will miss Wednesday’s season finale against the Raptors.

The Knicks said Anthony will be reevaluated in one month, by which time he could be healed, according to Mike Woodson. The Knicks had called it a “strain,’’ which is akin to a very minor tear. It’s conceivable the injury, which happened when he became entangled with Joe Johnson in a game against the Nets on April 2, could have worsened from playing through it for four games.

Anthony had two tears in his left shoulder after last season’s playoffs — the rotator cuff and labrum. He chose to rehab it and did so successfully. The rotator cuff is considered more serious than a labrum tear.

If Anthony did have surgery, it probably would affect his free agency because the healing process is several months. That’s why he’ll follow the same path as last season and told TNT he can’t wait to begin rehab.

“It’s hard, really hard,’’ Anthony said of missing the playoffs. “I have a lot to think about.”

Presumably he was referring to his future. His chances of remaining with the Knicks were greatly lifted with the hiring of Phil Jackson as president. As Anthony said Sunday, it was “definitely a big play for our organization, for the Knicks and for me.”

Anthony showed up in Brooklyn Tuesday night before the game, entered the locker room where he went around to shake every player’s hand but declined to speak to reporters.

“I feel bad for him more than anyone,’’ Woodson said before Tuesday night’s win.“He had the kind of season where he deserves to be in the playoffs. I feel bad about that.‘’

Anthony refused to take an MRI exam when the Knicks were still in the playoff race. They were eliminated Saturday night.

“Obviously he knew it was bothering him but he hung in there with us and tried to make this last push to the playoffs,’’ Woodson said. “He’ll be good to go in a month or so and we’ll see.’’

At the morning shootaround at Barclays Center, Woodson said Anthony was finished for the season, even though the results of his MRI were unknown.

Anthony finished the season averaging 27.4 points per game on 45.2 percent shooting in 77 games, averaging 38.7 minutes. He also shot a healthy 40 percent from 3-point land and hauled in a career-high 8.2 rebounds per game. He’s the first player since Shaquille O’Neal in 2002-03 to average at least 27 points and 8 boards.

Anthony has been bothered by a shoulder since April 2 when he became entangled with Joe Johnson of the Nets.

The Lakers have cap space to pursue Anthony but that seems unlikely. The Bulls, Rockets and Clippers will also have interest but need to pull off a sign-and-trade unless they can make deals to get under the cap.

Jackson made a rare road appearance sitting in a suite at Barclays and didn’t speak to reporters as he got into his black van afterward.